The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​ distribution, with a mean of 15 minutes and a standard deviation of 3.5...

The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​ distribution, with a mean of

minutes and a standard deviation of

minutes.

​(a) The automotive center guarantees customers that the service will take no longer than

minutes. If it does take​ longer, the customer will receive the service for​ half-price. What percent of customers receive the service for​ half-price?

​(b) If the automotive center does not want to give the discount to more than

of its​ customers, how long should it make the guaranteed time​ limit?

Click here to view the standard normal distribution table (page 1).

Click here to view the standard normal distribution table (page 2).

​(a) The percent of customers that receive the service for​ half-price is

​(Round to two decimal places as​ needed.)

​(b) The guaranteed time limit is

minutes.

​(Round up to the nearest​ minute.)